Problem: Simplify the following expression: $\dfrac{55x^4}{40x^4}$ You can assume $x \neq 0$.
Answer: $ \dfrac{55x^4}{40x^4} = \dfrac{55}{40} \cdot \dfrac{x^4}{x^4} $ To simplify $\frac{55}{40}$ , find the greatest common factor (GCD) of $55$ and $40$ $55 = 5 \cdot 11$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(55, 40) = 5 $ $ \dfrac{55}{40} \cdot \dfrac{x^4}{x^4} = \dfrac{5 \cdot 11}{5 \cdot 8} \cdot \dfrac{x^4}{x^4} $ $\phantom{ \dfrac{55}{40} \cdot \dfrac{4}{4}} = \dfrac{11}{8} \cdot \dfrac{x^4}{x^4} $ $ \dfrac{x^4}{x^4} = \dfrac{x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x} = 1 $ $ \dfrac{11}{8} \cdot 1 = \dfrac{11}{8} $